Question

How do you find the magnitude of YZ given Y(5,0) and Z(7,6)?

Answer 1

`bb(vec(YZ)) = ( (2), (6) ) \ \` and `\ \ abs(bb(vec(YZ))) = 2sqrt(10)`

Explanation:

We have `Y` and `Z` with coordinates `(5,0)` and `(7,6)` respectively.

So in vector notation we can write:

`bb(vec(OY)) = ( (5), (0) ) \ \` and `\ \ bb(vec(OZ)) = ( (7), (6) )`

We can calculate `abs(bb(vec(YZ)))` in several ways:

Method 1:

Using the coordinates along, we can apply pythagoras theorem:

`YZ^2 = (7-5)^2 + (6-0)^2`
`\ \ \ \ \ \ \ = 2^2 + 6^2`
`\ \ \ \ \ \ \ = 4+36`
`\ \ \ \ \ \ \ = 40`

And so `YZ = sqrt(40) = 2sqrt(10)`

Method 2:

Using vector notation we can calculate the vector `bb(vec(YZ))` and then calculate its magnitude.

We have:

`bb(vec(YZ)) = bb(vec(OZ)) - bb(vec(OY))`
`\ \ \ \ \ \ = ( (7), (6) ) - ( (5), (0) )`
`\ \ \ \ \ \ = ( (7-5), (6-0) )`
`\ \ \ \ \ \ = ( (2), (6) )`

And so:

`abs(bb(vec(YZ))) = sqrt(2^2+6^2)`
`\ \ \ \ \ \ \ \ = 2sqrt(10)`, as before.